What is the derivative of (2x/(x^2+5)) ?

The derivative of (2x/(x^2+5)) is (2(-x^2+5))/((x^2+5)^2)

What is the first derivative of (2x/(x^2+5)) ?

The first derivative of (2x/(x^2+5)) is (2(-x^2+5))/((x^2+5)^2)

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\frac{d}{d x} (\frac{2 x}{x ^{2} + 5})

\frac{2 ( - x ^{2} + 5 )}{( x ^{2} + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{x ^{2} + 5})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{x}{x ^{2} + 5})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 2 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 5 ) - \frac{d}{d x} ( x ^{2} + 5 ) x}{( x ^{2} + 5 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} + 5) = 2 x

= 2 \cdot \frac{1 \cdot ( x ^{2} + 5 ) - 2 xx}{( x ^{2} + 5 ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( x ^{2} + 5 ) - 2 xx}{( x ^{2} + 5 ) ^{2}} : \frac{2 ( - x ^{2} + 5 )}{( x ^{2} + 5 ) ^{2}}

= \frac{2 ( - x ^{2} + 5 )}{( x ^{2} + 5 ) ^{2}}

\int \frac{1}{32768} sin (8 x) d x

3 x y^{^{'}} - 2 y = \frac{x ^{3}}{y ^{2}}

x, 2 x, - x + 2

t e^{- 4 t} cos (5 t)

- x^{4}, x^{2} - 2 x

What is the derivative of (2x/(x^2+5)) ?
The derivative of (2x/(x^2+5)) is (2(-x^2+5))/((x^2+5)^2)
What is the first derivative of (2x/(x^2+5)) ?
The first derivative of (2x/(x^2+5)) is (2(-x^2+5))/((x^2+5)^2)